Granny knot (mathematics)

In knot theory, the granny knot is a composite knot obtained by taking the connected sum of two identical trefoil knots. It is closely related to the square knot, which can also be described as a connected sum of two trefoils. Because the trefoil knot is the simplest nontrivial knot, the granny knot and the square knot are the simplest of all composite knots.

The granny knot is the mathematical version of the common granny knot.

The granny knot can be constructed from two identical trefoil knots, which must either be both left-handed or both right-handed. Each of the two knots is cut, and then the loose ends are joined together pairwise. The resulting connected sum is the granny knot.

It is important that the original trefoil knots be identical to each another. If mirror-image trefoil knots are used instead, the result is a square knot.